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    <meta name="description" content="在上一节中，总结了各种定义特殊点的方法，这一节主要讲述如何定义各类直线形——直线，三角形和多边形．">
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          常用 tkz-euclide 命令（二）——直线形的定义方法
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    <div class="post-body" itemprop="articleBody"><p>在上一节中，总结了各种定义特殊点的方法，这一节主要讲述如何定义各类直线形——直线，三角形和多边形．</p>
<span id="more"></span>
<h2 id="1-定义直线形的方法"><a class="header-anchor" href="#1-定义直线形的方法"></a>1. 定义直线形的方法</h2>
<h3 id="1-1-定义直线"><a class="header-anchor" href="#1-1-定义直线"></a>1.1. 定义直线</h3>
<p>命令：<code>\tkzDefLine[&lt;options&gt;](A,B) or (A,B,C)  \tkzGetPoints&#123;P&#125;&#123;Q&#125; or \tkzGetPoint&#123;P&#125;</code></p>
<table>
<thead>
<tr>
<th>描述</th>
<th>默认长度</th>
<th>选项</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>B</mi></mrow><annotation encoding="application/x-tex">AB</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span></span> 的垂直平分线 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mi>Q</mi></mrow><annotation encoding="application/x-tex">PQ</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">PQ</span></span></span></span></td>
<td>正<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">△</mi><mi>A</mi><mi>B</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">\triangle ABP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">△</span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.13889em;">BP</span></span></span></span>、<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">△</mi><mi>A</mi><mi>B</mi><mi>Q</mi></mrow><annotation encoding="application/x-tex">\triangle ABQ</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">△</span><span class="mord mathnormal">A</span><span class="mord mathnormal">BQ</span></span></span></span></td>
<td>默认，或者 <code>mediator</code></td>
</tr>
<tr>
<td>过 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi></mrow><annotation encoding="application/x-tex">M</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">M</span></span></span></span> 的垂线 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>P</mi><mo>⊥</mo><mi>A</mi><mi>B</mi></mrow><annotation encoding="application/x-tex">MP\perp AB</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">MP</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⊥</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span></span></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>P</mi><mo>=</mo><mi>A</mi><mi>B</mi></mrow><annotation encoding="application/x-tex">MP=AB</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">MP</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span></span></td>
<td><code>perpendicular=through M</code> <br />或 <code>orthogonal=through M</code></td>
</tr>
<tr>
<td>过 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi></mrow><annotation encoding="application/x-tex">M</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">M</span></span></span></span> 的平行线 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>P</mi><mo>∥</mo><mi>A</mi><mi>B</mi></mrow><annotation encoding="application/x-tex">MP \parallel AB</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">MP</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∥</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span></span></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><mi>M</mi><mi>P</mi></mrow><mo stretchy="true">→</mo></mover><mo>=</mo><mover accent="true"><mrow><mi>A</mi><mi>B</mi></mrow><mo stretchy="true">→</mo></mover></mrow><annotation encoding="application/x-tex">\overrightarrow{MP}=\overrightarrow{AB}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2053em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.2053em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">MP</span></span></span><span class="svg-align" style="top:-3.6833em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="height:0.522em;min-width:0.888em;"><svg xmlns="http://www.w3.org/2000/svg" width='400em' height='0.522em' viewBox='0 0 400000 522' preserveAspectRatio='xMaxYMin slice'><path d='M0 241v40h399891c-47.3 35.3-84 78-110 128
-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20
 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7
 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85
-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5
-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67
 151.7 139 205zm0 0v40h399900v-40z'/></svg></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2053em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.2053em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span><span class="svg-align" style="top:-3.6833em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="height:0.522em;min-width:0.888em;"><svg xmlns="http://www.w3.org/2000/svg" width='400em' height='0.522em' viewBox='0 0 400000 522' preserveAspectRatio='xMaxYMin slice'><path d='M0 241v40h399891c-47.3 35.3-84 78-110 128
-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20
 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7
 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85
-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5
-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67
 151.7 139 205zm0 0v40h399900v-40z'/></svg></span></span></span></span></span></span></span></span></span>．</td>
<td><code>parallel=through M</code></td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∠</mi><mi>A</mi><mi>B</mi><mi>C</mi></mrow><annotation encoding="application/x-tex">\angle ABC</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6922em;"></span><span class="mord">∠</span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span></span></span></span> 的角平分线 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">BP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">BP</span></span></span></span></td>
<td>很长，建议<br />使用 <code>normed</code></td>
<td><code>bisector</code></td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∠</mi><mi>A</mi><mi>B</mi><mi>C</mi></mrow><annotation encoding="application/x-tex">\angle ABC</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6922em;"></span><span class="mord">∠</span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span></span></span></span> 的邻补角 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∠</mi><msup><mi>A</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mi>B</mi><mi>C</mi></mrow><annotation encoding="application/x-tex">\angle A&#x27;BC</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7519em;"></span><span class="mord">∠</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span></span></span></span> 的平分线 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">BP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">BP</span></span></span></span></td>
<td>很长，建议<br />使用 <code>normed</code></td>
<td><code>bisector out</code></td>
</tr>
<tr>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td>选项：变换系数</td>
<td></td>
<td><code>K=1</code></td>
</tr>
<tr>
<td>选项：正交化</td>
<td></td>
<td><code>normed</code></td>
</tr>
</tbody>
</table>
<h3 id="1-2-定义切线"><a class="header-anchor" href="#1-2-定义切线"></a>1.2. 定义切线</h3>
<table>
<thead>
<tr>
<th>描述</th>
<th>命令</th>
</tr>
</thead>
<tbody>
<tr>
<td>过 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⊙</mo><mi>O</mi></mrow><annotation encoding="application/x-tex">\odot O</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em;"></span><span class="mord">⊙</span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span></span></span></span> 上点 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span></span></span></span> 的切线 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">AP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span></td>
<td><code>\tkzDefTangent[at=A](O)  \tkzGetPoint&#123;P&#125;</code></td>
</tr>
<tr>
<td>过<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⊙</mo><mi>O</mi></mrow><annotation encoding="application/x-tex">\odot O</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em;"></span><span class="mord">⊙</span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span></span></span></span> 外点 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span></span></span></span> 的切线 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">AP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span>、<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>Q</mi></mrow><annotation encoding="application/x-tex">AQ</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal">Q</span></span></span></span></td>
<td><code>\tkzDefTangent[from=A](O, K)  \tkzGetPoints&#123;P&#125;&#123;Q&#125;</code> <br />或 <code>\tkzDefTangent[from with R=A](O, r cm)\tkzGetPoints&#123;P&#125;&#123;Q&#125;</code></td>
</tr>
</tbody>
</table>
<h3 id="1-3-定义三角形"><a class="header-anchor" href="#1-3-定义三角形"></a>1.3. 定义三角形</h3>
<p>命令：<code>\tkzDefTriangle[&lt;options&gt;](A,B)  \tkzGetPoint&#123;C&#125;</code></p>
<table>
<thead>
<tr>
<th>种类</th>
<th>选项</th>
</tr>
</thead>
<tbody>
<tr>
<td>已知两个角（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∠</mi><mi>A</mi><mo>=</mo><mi>α</mi><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\angle A=\alpha \degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6922em;"></span><span class="mord">∠</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.0037em;">α</span><span class="mord">°</span></span></span></span>，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∠</mi><mi>B</mi><mo>=</mo><mi>β</mi><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\angle B=\beta \degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6922em;"></span><span class="mord">∠</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.05278em;">β</span><span class="mord">°</span></span></span></span>）</td>
<td><code>two angles=α and β</code></td>
</tr>
<tr>
<td>等边三角形</td>
<td><code>equilateral</code></td>
</tr>
<tr>
<td>特殊直角三角形（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>B</mi><mo>=</mo><mn>2</mn><mi>B</mi><mi>C</mi></mrow><annotation encoding="application/x-tex">AB=2BC</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">2</span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span></span></span></span>，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∡</mi><mi>A</mi><mi>B</mi><mi>C</mi><mo>=</mo><mn>90</mn><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\measuredangle ABC=90 \degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6922em;"></span><span class="mord amsrm">∡</span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">90°</span></span></span></span>）</td>
<td><code>half</code></td>
</tr>
<tr>
<td>等腰直角三角形（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>C</mi><mo>=</mo><mi>B</mi><mi>C</mi></mrow><annotation encoding="application/x-tex">AC=BC</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span></span></span></span>，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∡</mi><mi>A</mi><mi>C</mi><mi>B</mi><mo>=</mo><mn>90</mn><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\measuredangle ACB=90\degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6922em;"></span><span class="mord amsrm">∡</span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">CB</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">90°</span></span></span></span>）</td>
<td><code>isosceles right</code></td>
</tr>
<tr>
<td>勾股三角形（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>B</mi><mo>:</mo><mi>B</mi><mi>C</mi><mo>:</mo><mi>A</mi><mi>C</mi><mo>=</mo><mn>4</mn><mo>:</mo><mn>3</mn><mo>:</mo><mn>5</mn></mrow><annotation encoding="application/x-tex">AB:BC:AC=4:3:5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">4</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">5</span></span></span></span>）</td>
<td><code>pythagore</code> 或 <code>pythagoras</code> 或 <code>egyptian</code></td>
</tr>
<tr>
<td>含有 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>30</mn><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">30 \degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">30°</span></span></span></span> 的直角三角形（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∠</mi><mi>A</mi><mo>=</mo><mn>30</mn><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\angle A=30 \degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6922em;"></span><span class="mord">∠</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">30°</span></span></span></span>，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∠</mi><mi>B</mi><mo>=</mo><mn>90</mn><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\angle B=90 \degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6922em;"></span><span class="mord">∠</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">90°</span></span></span></span>）</td>
<td><code>school</code></td>
</tr>
<tr>
<td>黄金三角形（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∠</mi><mi>A</mi><mo>=</mo><mn>36</mn><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\angle A=36 \degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6922em;"></span><span class="mord">∠</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">36°</span></span></span></span>，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∠</mi><mi>B</mi><mo>=</mo><mi mathvariant="normal">∠</mi><mi>C</mi><mo>=</mo><mn>72</mn><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\angle B=\angle C=72\degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6922em;"></span><span class="mord">∠</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6922em;"></span><span class="mord">∠</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">72°</span></span></span></span>）</td>
<td><code>gold</code></td>
</tr>
<tr>
<td>黄金三角形（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∠</mi><mi>C</mi><mo>=</mo><mn>36</mn><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\angle C=36 \degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6922em;"></span><span class="mord">∠</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">36°</span></span></span></span>，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∠</mi><mi>A</mi><mo>=</mo><mi mathvariant="normal">∠</mi><mi>B</mi><mo>=</mo><mn>72</mn><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\angle A=\angle B=72\degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6922em;"></span><span class="mord">∠</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6922em;"></span><span class="mord">∠</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">72°</span></span></span></span>）</td>
<td><code>euclid</code></td>
</tr>
<tr>
<td>黄金矩形的一半（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∠</mi><mi>B</mi><mo>=</mo><mn>90</mn><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\angle B=90\degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6922em;"></span><span class="mord">∠</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">90°</span></span></span></span>，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>A</mi><mi>B</mi></mrow><mrow><mi>B</mi><mi>C</mi></mrow></mfrac></mstyle><mo>=</mo><mi>φ</mi></mrow><annotation encoding="application/x-tex">\dfrac{AB}{BC}=\varphi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.0463em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3603em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">φ</span></span></span></span>）</td>
<td><code>golden</code></td>
</tr>
<tr>
<td>胡夫三角形（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>B</mi><mo>:</mo><mi>B</mi><mi>C</mi><mo>:</mo><mi>A</mi><mi>C</mi><mo>=</mo><mn>2</mn><mo>:</mo><mi>φ</mi><mo>:</mo><mi>φ</mi></mrow><annotation encoding="application/x-tex">AB:BC:AC=2:\varphi:\varphi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">φ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">φ</span></span></span></span>）</td>
<td><code>cheops</code></td>
</tr>
<tr>
<td></td>
<td></td>
</tr>
<tr>
<td>选项：给出关于 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>B</mi></mrow><annotation encoding="application/x-tex">AB</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span></span> 的对称点</td>
<td><code>swap</code></td>
</tr>
</tbody>
</table>
<h3 id="1-4-定义特殊三角形"><a class="header-anchor" href="#1-4-定义特殊三角形"></a>1.4. 定义特殊三角形</h3>
<p>命令：<code>\tkzDefSpcTriangle[&lt;options&gt;, name=M_](A,B,C)&#123;A,B,C&#125;</code>，新三角形的三个顶点依次为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>M</mi><mi>A</mi></msub></mrow><annotation encoding="application/x-tex">M_A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">M</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.109em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">A</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>、<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>M</mi><mi>B</mi></msub></mrow><annotation encoding="application/x-tex">M_B</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">M</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.109em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05017em;">B</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>、<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>M</mi><mi>C</mi></msub></mrow><annotation encoding="application/x-tex">M_C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">M</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.109em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07153em;">C</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>，</p>
<table>
<thead>
<tr>
<th>描述</th>
<th>对应的「心」</th>
<th>选项</th>
</tr>
</thead>
<tbody>
<tr>
<td></td>
<td>内心</td>
<td><code>in</code> 或 <code>incentral</code></td>
</tr>
<tr>
<td>旁心三角形</td>
<td></td>
<td><code>ex</code> 或 <code>excentral</code></td>
</tr>
<tr>
<td>内切点三角形</td>
<td>Gergonne 点</td>
<td><code>intouch</code> 或 <code>contact</code></td>
</tr>
<tr>
<td>旁切点三角形</td>
<td>Nagel 点</td>
<td><code>extouch</code></td>
</tr>
<tr>
<td>中点三角形</td>
<td>重心</td>
<td><code>centroid</code> 或 <code>medial</code></td>
</tr>
<tr>
<td>垂足三角形</td>
<td>垂心</td>
<td><code>orthic</code></td>
</tr>
<tr>
<td>九点圆和旁切圆切点三角形</td>
<td></td>
<td><code>feuerbach</code></td>
</tr>
<tr>
<td>欧拉三角形（由顶点与垂心的中点构成）</td>
<td></td>
<td><code>euler</code></td>
</tr>
<tr>
<td>外接圆外切三角形</td>
<td></td>
<td><code>tangential</code></td>
</tr>
<tr>
<td>类似中线的交点三角形</td>
<td>类似重心</td>
<td><code>symmedial</code></td>
</tr>
<tr>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td>选项：名称</td>
<td></td>
<td><code>name=...</code></td>
</tr>
</tbody>
</table>
<h3 id="1-5-定义特殊多边形"><a class="header-anchor" href="#1-5-定义特殊多边形"></a>1.5. 定义特殊多边形</h3>
<table>
<thead>
<tr>
<th>图形</th>
<th>命令</th>
</tr>
</thead>
<tbody>
<tr>
<td>正方形（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>B</mi></mrow><annotation encoding="application/x-tex">AB</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span></span> 为边）</td>
<td><code>\tkzDefSquare(A,B)  \tkzGetPoints&#123;C&#125;&#123;D&#125;</code></td>
</tr>
<tr>
<td>矩形（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>C</mi></mrow><annotation encoding="application/x-tex">AC</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span></span></span></span> 为对角线）</td>
<td><code>\tkzDefRectangle(A,C) \tkzGetPoints&#123;B&#125;&#123;D&#125;</code></td>
</tr>
<tr>
<td>平行四边形</td>
<td><code>\tkzDefParallelogram(A,B,C)  \tkzGetPoint&#123;D&#125;</code></td>
</tr>
<tr>
<td>黄金矩形（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>A</mi><mi>B</mi></mrow><mrow><mi>B</mi><mi>C</mi></mrow></mfrac></mstyle><mo>=</mo><mi>φ</mi></mrow><annotation encoding="application/x-tex">\dfrac{AB}{BC}=\varphi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.0463em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3603em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">φ</span></span></span></span>）</td>
<td><code>\tkzDefGoldRectangle(A,B)  \tkzGetPoints&#123;C&#125;&#123;D&#125;</code></td>
</tr>
</tbody>
</table>
<h3 id="1-6-定义正多边形"><a class="header-anchor" href="#1-6-定义正多边形"></a>1.6. 定义正多边形</h3>
<p>命令：<code>\tkzDefRegPolygon[&lt;options&gt;](A,B)</code></p>
<table>
<thead>
<tr>
<th>描述</th>
<th>选项</th>
</tr>
</thead>
<tbody>
<tr>
<td>第一个字母为中心（默认）</td>
<td><code>center</code></td>
</tr>
<tr>
<td>两个字母为相邻顶点</td>
<td><code>side</code></td>
</tr>
<tr>
<td>边数</td>
<td><code>sides=5</code></td>
</tr>
<tr>
<td>顶点命名（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">P_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>、<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">P_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>、…）</td>
<td><code>name=P</code></td>
</tr>
</tbody>
</table>
<h2 id="2-绘制直线形的方法"><a class="header-anchor" href="#2-绘制直线形的方法"></a>2. 绘制直线形的方法</h2>
<h3 id="2-1-绘制直线"><a class="header-anchor" href="#2-1-绘制直线"></a>2.1. 绘制直线</h3>
<p>绘制一条直线：<code>\tkzDrawLine[&lt;options&gt;](A,B)</code></p>
<p>绘制多条直线：<code>\tkzDrawLines[&lt;options&gt;](A,B C,D ...)</code></p>
<p>自定义直线的样式：<code>\tkzSetUpLine[&lt;options&gt;]</code></p>
<table>
<thead>
<tr>
<th>样式</th>
<th>默认选项</th>
</tr>
</thead>
<tbody>
<tr>
<td>样式</td>
<td><code>style=solid</code>（或 <code>dashed</code>、<code>densely dashed</code>、<code>dotted</code>、<code>densely dotted</code>）</td>
</tr>
<tr>
<td>粗细</td>
<td><code>line width=0.4pt</code></td>
</tr>
<tr>
<td>颜色</td>
<td><code>color=black</code></td>
</tr>
<tr>
<td>延长</td>
<td><code>add= .2 and .2</code></td>
</tr>
</tbody>
</table>
<h3 id="2-2-绘制线段"><a class="header-anchor" href="#2-2-绘制线段"></a>2.2. 绘制线段</h3>
<p>绘制一条线段：<code>\tkzDrawSegment[&lt;options&gt;](A,B)</code>（相当于 <code>\draw (A)--(B)</code>）</p>
<p>绘制多条线段：<code>\tkzDrawSegments[&lt;options&gt;](A,B C,D ...)</code></p>
<h3 id="2-3-（定义并）绘制三角形"><a class="header-anchor" href="#2-3-（定义并）绘制三角形"></a>2.3. （定义并）绘制三角形</h3>
<p>命令：<code>\tkzDrawTriangle[&lt;options&gt;](A,B)  \tkzGetPoint&#123;C&#125;</code></p>
<h3 id="2-4-（定义并）绘制正方形"><a class="header-anchor" href="#2-4-（定义并）绘制正方形"></a>2.4. （定义并）绘制正方形</h3>
<p>命令：<code>\tkzDrawSquare[&lt;options&gt;](A,B)  \tkzGetPoints&#123;C&#125;&#123;D&#125;</code></p>
<h3 id="2-5-（定义并）绘制黄金矩形"><a class="header-anchor" href="#2-5-（定义并）绘制黄金矩形"></a>2.5. （定义并）绘制黄金矩形</h3>
<p>命令：<code>\tkzDrawGoldRectangle[&lt;options&gt;](A,B)  \tkzGetPoints&#123;C&#125;&#123;D&#125;</code></p>
<h3 id="2-6-绘制多边形"><a class="header-anchor" href="#2-6-绘制多边形"></a>2.6. 绘制多边形</h3>
<p>命令：<code>\tkzDrawPolygon[&lt;options&gt;](A,B,C,...)</code></p>
<h3 id="2-7-绘制多边形链"><a class="header-anchor" href="#2-7-绘制多边形链"></a>2.7. 绘制多边形链</h3>
<p>命令：<code>\tkzDrawPolySeg[&lt;options&gt;](A,B,C,...)</code></p>
<h2 id="3-填充直线形的方法"><a class="header-anchor" href="#3-填充直线形的方法"></a>3. 填充直线形的方法</h2>
<h3 id="3-1-填充多边形"><a class="header-anchor" href="#3-1-填充多边形"></a>3.1. 填充多边形</h3>
<p>命令：<code>\tkzFillPolygon[&lt;options&gt;](A,B,C,...)</code></p>
<h2 id="4-标记直线形的方法"><a class="header-anchor" href="#4-标记直线形的方法"></a>4. 标记直线形的方法</h2>
<h3 id="4-1-标记直线"><a class="header-anchor" href="#4-1-标记直线"></a>4.1. 标记直线</h3>
<p>命令：<code>\tkzLabelLine[&lt;options&gt;](A,B)&#123;&lt;text support tex&gt;&#125;</code></p>
<table>
<thead>
<tr>
<th>描述</th>
<th>选项</th>
</tr>
</thead>
<tbody>
<tr>
<td>相对位置</td>
<td><code>pos=.5</code></td>
</tr>
<tr>
<td>位置</td>
<td><code>above/below + left/right</code></td>
</tr>
<tr>
<td>颜色</td>
<td><code>black</code></td>
</tr>
</tbody>
</table>
<h3 id="4-2-标记线段"><a class="header-anchor" href="#4-2-标记线段"></a>4.2. 标记线段</h3>
<p>标记一条线段：<code>\tkzLabelSegment[&lt;options&gt;](A,B)</code></p>
<p>标记多条线段：<code>\tkzLabelSegments[&lt;options&gt;](A,B C,D ...)</code></p>
<p>选项和直线相同．</p>
<h3 id="4-3-用符号标记线段"><a class="header-anchor" href="#4-3-用符号标记线段"></a>4.3. 用符号标记线段</h3>
<p>标记一条线段：<code>\tkzMarkSegment[mark=&lt;mark option&gt;, &lt;other options&gt;](A,B)</code></p>
<p>标记多条线段：<code>\tkzMarkSegments[mark=&lt;mark option&gt;, &lt;other options&gt;](A,B C,D ...)</code></p>
<table>
<thead>
<tr>
<th>符号</th>
<th>标记选项</th>
</tr>
</thead>
<tbody>
<tr>
<td>部分字母</td>
<td><code>o</code>、<code>s</code>、<code>x</code>、<code>z</code></td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∞</mi></mrow><annotation encoding="application/x-tex">\infty</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord">∞</span></span></span></span></td>
<td><code>oo</code></td>
</tr>
<tr>
<td>直竖线</td>
<td>`</td>
</tr>
<tr>
<td>斜竖线</td>
<td>`s</td>
</tr>
</tbody>
</table>
<table>
<thead>
<tr>
<th>描述</th>
<th>其它选项</th>
</tr>
</thead>
<tbody>
<tr>
<td>相对位置</td>
<td><code>pos=.5</code></td>
</tr>
<tr>
<td>大小</td>
<td><code>size=4pt</code></td>
</tr>
<tr>
<td>颜色</td>
<td><code>black</code></td>
</tr>
</tbody>
</table>

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